Certified strong-coupling reduced dynamics
For a specified non-Gaussian or initially correlated system–bath model, construct computationally tractable reduced-process approximations with certified finite-time error, controlled memory truncation and positivity on the stated preparation or intervention d
Problem statement
For a specified non-Gaussian or initially correlated system–bath model, construct computationally tractable reduced-process approximations with certified finite-time error, controlled memory truncation and positivity on the stated preparation or intervention domain.
Lean 4
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Background
At strong coupling, weak-coupling master equations can be inaccurate and the reduced equilibrium state need not be the bare Gibbs state. Strong coupling alone does not destroy complete positivity: unitary joint evolution from a fixed factorized bath state induces a CPTP map on all system inputs at any coupling. With initial correlations, a single map on arbitrary system states may be inappropriate; specify the preparation family or an intervention-based process instead.
What is known: Exact influence functionals and process tensors already formulate reduced dynamics beyond weak coupling. Reaction-coordinate mappings can improve the residual-bath treatment but do not guarantee weak residual coupling. HEOM and related methods admit systematically converged calculations in suitable bath models; finite hierarchy and time discretizations need error control. Polaron methods and the Hamiltonian of mean force address further dynamical and equilibrium regimes.
The frontier is efficient approximation with certificates, not existence of a universal exact formalism. Specify a bath family, initial correlations, accessible interventions and energy bookkeeping; prove error and resource bounds for memory/compression truncations, or establish obstructions. Agreement with equilibrium thermodynamics does not by itself certify transient dynamics. Related: O2, O4, O5, O8.
Progress & source assessment
Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.
- [1]de Vega & Alonso, 'Dynamics of non-Markovian open quantum systems', Rev. Mod. Phys. 89, 015001 (2017) link
- [2]Rivas, 'Strong coupling thermodynamics of open quantum systems', PRL 124, 160601 (2020) link
- [3]Pollock et al., 'Operational Markov condition for quantum processes', PRL 120, 040405 (2018) link
Recorded progress
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